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((short description|In computing, a condition where an expression does not have a correct value))
((Other uses|Undefined (disambiguation)((!))Undefined))
((Refimprove|date=March 2010))
((Use dmy dates|date=December 2021|cs1-dates=y))
In computing (particularly, in [[Computer programming|programming]]), '''undefined value''' is a condition where an [[expression (programming)|expression]] does not have a correct [[value (computer science)|value]], although it is [[syntax (programming languages)|syntactically]] correct. An undefined value must not be confused with [[empty string]], [[Boolean data type|Boolean]] "false" or other "empty" (but defined) values. Depending on circumstances, evaluation to an undefined value may lead to [[exception (programming)|exception]] or [[undefined behaviour]], but in some [[programming language]]s undefined values can occur during a normal, predictable course of [[program (computing)|program]] execution.

[[Dynamic typing|Dynamically typed]] languages usually treat undefined values explicitly when possible. For instance, [[Perl]] has <code>undef</code> operator<ref name="Perl_2009_Undef"/> which can "assign" such value to a variable. In other type systems an undefined value can mean an unknown, unpredictable value, or merely a program failure on attempt of its evaluation. Nullable types offer an intermediate approach; see [[#Undefined value and nullable types|below]].

== Handling ==
The value of a [[partial function]] is undefined when its argument is out of its [[domain of definition]]. This include numerous [[arithmetic]]al cases such as [[division by zero]], [[square root]] or [[logarithm]] of a [[negative number]] etc. Another common example is accessing an [[array data structure|array]] with an index which is out of bounds, as is the value in an [[associative array]] for a key which it does not contain. There are various ways that these situations are handled in practice:

=== Reserved value ===
((main|Nullable type|Sentinel value|NaN))

In applications where undefined values must be handled gracefully, it is common to reserve a special null value which is distinguishable from normal values. This resolves the difficulty by creating a defined value to represent the formerly undefined case.  There are many examples of this:
* The C [[C file input/output|standard I/O library]] reserves the special value <code>[[End-of-file|EOF]]</code> to indicate that no more input is available.  The <code>getchar()</code> function returns the next available input character, or <code>EOF</code> if there is no more available. (The [[ASCII]] character code defines a [[null character]] for this purpose, but the standard I/O library wishes to be able to send and receive null characters, so it defines a separate <code>EOF</code> value.)
* The [[IEEE 754]] floating-point arithmetic standard defines a special "[[not a number]]" value which is returned when an [[arithmetic]] operation has no defined value.  Examples are [[division by zero]], or the [[square root]] or [[logarithm]] of a [[negative number]].
* [[Structured Query Language]] has a special <code>[[Null (SQL)|NULL]]</code> value to indicate missing data.
* The Perl language lets the definedness of an expression be checked via the <code>defined()</code> predicate.<ref name="Perl_2009_Defined"/>
* Many programming languages support the concept of a [[null pointer]] distinct from any valid pointer, and often used as an error return.
* Some languages allow most types to be nullable, for example [[C Sharp (programming language)|C#]].<ref name="Carr_2006"/>
* Most [[Unix]] [[system call]]s return the special value &minus;1 to indicate failure.

While [[dynamically typed]] languages often ensure that [[uninitialized variable]]s default to a null value, statically typed values often do not, and distinguish null values (which are well-defined) from uninitialized values (which are not).((r|Carr_2006))

=== Exception handling ===
Some programming languages have a concept of [[exception handling]] for dealing with failure to return a value.  The function returns in a defined way, but it does not return a value, so there is no need to invent a special value to return.

A variation on this is [[signal handling]], which is done at the operating system level and not integrated into a programming language.  Signal handlers can attempt some forms of recovery, such as terminating part of a computation, but without as much flexibility as fully integrated exception handling.

=== Non-returning functions ===
((main|Bottom type))

A function which never returns has an undefined value because the value can never be observed.  Such functions are formally assigned the [[bottom type]], which has no values.  Examples fall into two categories:
* Functions which [[infinite loop|loop forever]].  This may arise deliberately, or as a result of a search for something which will never be found.  (For example, in the case of failed [[μ operator]] in a [[partial recursive function]].)
* Functions which terminate the computation, such as the [[Exit (system call)|<code>exit</code> system call]].  From within the program, this is indistinguishable from the preceding case, but it makes a difference to the invoker of the program.

=== Undefined behaviour ===
((main|Undefined behaviour))

All of the preceding  methods of handling undefined values require that the undefinedness be detected.  That is, the called function determines that it cannot return a normal result and takes some action to notify the caller.  At the other end of the spectrum, ''undefined behaviour'' places the onus on the caller to avoid calling a function with arguments outside of its domain.  There is no limit on what might happen.  At best, an easily detectable [[Crash (computing)|crash]]; at worst, a subtle error in a seemingly unrelated computation.

(The formal definition of "undefined behaviour" includes even more extreme possibilities, including things like "[[Halt and Catch Fire (computing)|halt and catch fire]]" and "make demons fly out of your nose".<ref name="Catb"/>)

The classic example is a [[dangling pointer]] reference. It is very fast to [[dereference]] a valid [[pointer (computer programming)|pointer]], but can be very complex to determine if a pointer is valid. Therefore, computer hardware and low-level languages such as [[C (programming language)|C]] do not attempt to validate pointers before dereferencing them, instead passing responsibility to the programmer. This offers speed at the expense of safety.

=== Undefined value ''sensu stricto'' ===
The strict definition of an undefined value is a superficially valid (non-null) output which is meaningless but does not trigger undefined behaviour. For example, passing a negative number to the [[fast inverse square root]] function will produce a number. Not a very useful number, but the computation will complete and return ''something''.

Undefined values occur particularly often in hardware. If a wire is not carrying useful information, it still exists and has some voltage level. The voltage should not be abnormal (e.g. not a damaging [[overvoltage]]), but the particular [[logic level]] is unimportant.

The same situation occurs in software when a [[data buffer]] is provided but not completely filled. For example, the C library <code>[[strftime]]</code> function converts a timestamp to human-readable form in a supplied output buffer. If the output buffer is not large enough to hold the result, an error is returned and the buffer's contents are undefined.

In the other direction, the [[open (system call)|<code>open</code> system call]] in [[POSIX]] takes three arguments: a file name, some flags, and a file mode.  The file mode is only used if the flags include <code>O_CREAT</code>. It is common to use a two-argument form of <code>open</code>, which provides an undefined value for the file mode, when <code>O_CREAT</code> is omitted.

Sometimes it is useful to work with such undefined values in a limited way. The overall computation can still be well-defined if the undefined value is later ignored.

As an example of this, the C language permits converting a pointer to an integer, although the numerical value of that integer is undefined. It may still be useful for debugging, for comparing two pointers for equality, or for creating an [[XOR linked list]].

Safely handling undefined values is important in [[optimistic concurrency control]] systems, which detect [[race condition]]s after the fact. For example, reading a [[shared variable]] protected by [[seqlock]] will produce an undefined value ''before'' determining that a race condition happened. It will then discard the undefined data and retry the operation. This produces a defined result as long as the operations performed on the undefined values do not produce full-fledged undefined behaviour.

Other examples of undefined values being useful are [[random number generator]]s and [[hash function]]s. The specific values returned are undefined, but they have well-defined properties and may be used without error.

== Notation ==
In [[computability theory]], undefinedness of an expression is denoted as ''expr''↑, and definedness as ''expr''↓.

== See also ==
* [[Defined and undefined]] (mathematics)
* [[Null (SQL)]]

== References ==
((Reflist|refs=
<ref name="Perl_2009_Undef">((cite web |title=undef |date=2009-09-25 |work=Perl 5 documentation |url=http://perldoc.perl.org/functions/undef.html |access-date=2010-03-26))</ref>
<ref name="Perl_2009_Defined">((cite web |title=defined |date=2009-09-25 |work=Perl 5 documentation |url=http://perldoc.perl.org/functions/defined.html |access-date=2010-03-26))</ref>
<ref name="Carr_2006">((cite web |title=C# Nullable Numeric Data Types |author-first=Richard |author-last=Carr |date=2006-10-01 |work=C# Fundamentals tutorial |url=http://www.blackwasp.co.uk/CSharpNullableDataTypes.aspx |access-date=2010-03-27))</ref>
<ref name="Catb">((cite web |title=Nasal demons |website=[[Jargon File]] |url=http://catb.org/jargon/html/N/nasal-demons.html |access-date=2014-06-12))</ref>
))

[[Category:Software anomalies]]
[[Category:Theory of computation]]

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